Algebra worksheet — GCSE Foundation

1.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

2.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

3.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

4.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

5.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

6.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

7.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

8.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

9.Solve the inequality 6x ≥ 18.

10.Which of these equations is equivalent to 5x − 2 = 3x + 8?

11.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

12.Which of these is an equation, rather than an expression, a formula or an identity?

13.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

14.Work out the gradient of the straight line with equation 2x + y = 8.

15.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?